We examine the role of GBFs and generalized
plateaued functions within
cocyclic design theory [1]}, [2]}.
Some requisite definitions follow.
Let \(G\)  and \(U\)  be finite groups, with \(U\) 
abelian. A map
\(\psi \colon G\times G\rightarrow U\)  such that
\(\psi (a,b)\psi (ab,c)=\psi (a,bc)\psi (b,c)\quad \forall \, a,b,c\in G\) 
